The US has confirmed that North Korea tested a long-range missile which some experts believe could reach Alaska.
Secretary of State Rex Tillerson called it a "new escalation of the threat" and warned that Washington "will never accept a nuclear-armed North Korea".
Pyongyang claimed on Tuesday to have successfully tested an intercontinental ballistic missile (ICBM).
However, most experts believe that the North does not yet have long-range nuclear weapon capabilities.
In response the US and South Korea conducted a joint military exercise on Wednesday.
A statement by the two countries' militaries warned that "self-restraint, which is a choice, is all that separates armistice and war" and that their drills showed "we are able to change our choice".
The two Koreas are technically still at war as the 1950-1953 Korean War ended in an armistice.
Mr Tillerson said "global action is required to stop a global threat" and warned that any nation that provided economic or military benefits to the North, or failed to fully implement UN Security Council resolution, was "aiding and abetting a dangerous regime".
The US has asked for an urgent meeting of the UN Security Council to discuss the issue. A closed-door session of the 15-member body is expected later on Wednesday.